Use the improved Eulers method with step size h 01 to appro

Use the improved Euler\'s method with step size h = 0.1 to approximate to five decimal places the values of the following differential equation on the given interval with the given initial condition xy\'(x) = 3x -2y, y(2) = 3, 2 lessthanorequalto x lessthanorequalto 4 Find the exact solution and make (print in Microsoft Word)) a table showing the approximate and the exact solution.

Solution

f(x,y)=(3x-2y)/x

y(2)=3

h=0.1

upto y(4)

	Improved Euler\'s Method
x0 =	2	y0 =	3	h=	0.1
x(n)	y(n)	f(x(n),y(n))	ye	y(n+1) = y(n)+(h/2)*(f(x(n),y(n))+f(x(n)+h,ye))
2	3	0	3	3.007142857
2.1	3.007142857	0.136054422	3.020748299	3.027257267			ye = y(n)+hf(x(n),y(n))
2.2	3.027257267	0.24794794	3.05205206	3.058034782
2.3	3.058034782	0.34083932	3.092118714	3.097658632
2.4	3.097658632	0.418617806	3.139520413	3.144683177
2.5	3.144683177	0.484253458	3.193108523	3.197946497
2.6	3.197946497	0.540041156	3.251950613	3.256506092
2.7	3.256506092	0.587773265	3.315283419	3.319590967
2.8	3.319590967	0.628863595	3.382477326	3.386565492
2.9	3.386565492	0.664437592	3.453009251	3.456901855
3	3.456901855	0.695398763	3.526441732	3.530158831
3.1	3.530158831	0.722478174	3.602406648	3.605965276
3.2	3.605965276	0.746271703	3.680592446	3.684007186
3.3	3.684007186	0.767268372	3.760734023	3.764017452
3.4	3.764017452	0.785872087	3.842604661	3.845767701
3.5	3.845767701	0.802418457	3.926009546	3.929061743
3.6	3.929061743	0.817187921	4.010780535	4.013730281
3.7	4.013730281	0.830416064	4.096771887	4.099626603
3.8	4.099626603	0.842301788	4.183856782	4.186623062
3.9	4.186623062	0.853013815	4.271924443	4.274608176
4	4.274608176	0.862695912	4.360877767	4.363484235
		y(4)=	4.274608176